Question

Trisha's work to verify the identity (a + bl(a b) is shown below:
Step 1: a(a - b) + b(a - b)
Step 2: a? ab + ab + b 2
Step 3: a? + b2
Given that she made an error, in which step did she make her first error?

Answer 1

Answer:

Step 1: Draw a square and cut into 3 parts.

Step 1: Draw a square and cut into 3 parts.Step 2: There are 1 hided square green and 2 rectangles (pink, blue)

Step 1: Draw a square and cut into 3 parts.Step 2: There are 1 hided square green and 2 rectangles (pink, blue)Step 3: Area of the full square = a 2−b 2

Step 1: Draw a square and cut into 3 parts.Step 2: There are 1 hided square green and 2 rectangles (pink, blue)Step 3: Area of the full square = a 2−b 2 Step 4: Now we have to find the area of rectangle as shown in the figure.

Step 1: Draw a square and cut into 3 parts.Step 2: There are 1 hided square green and 2 rectangles (pink, blue)Step 3: Area of the full square = a 2−b 2 Step 4: Now we have to find the area of rectangle as shown in the figure.Step 5: Consider the area of pink rectangle = length × breadth = a(a−b)

Step 1: Draw a square and cut into 3 parts.Step 2: There are 1 hided square green and 2 rectangles (pink, blue)Step 3: Area of the full square = a 2−b 2 Step 4: Now we have to find the area of rectangle as shown in the figure.Step 5: Consider the area of pink rectangle = length × breadth = a(a−b)Step 6: Area of blue rectangle = b(a−b)

Step 1: Draw a square and cut into 3 parts.Step 2: There are 1 hided square green and 2 rectangles (pink, blue)Step 3: Area of the full square = a 2−b 2 Step 4: Now we have to find the area of rectangle as shown in the figure.Step 5: Consider the area of pink rectangle = length × breadth = a(a−b)Step 6: Area of blue rectangle = b(a−b) Step 7: Area of full square = area of pink rectangle + area of blue rectangle.

Step 1: Draw a square and cut into 3 parts.Step 2: There are 1 hided square green and 2 rectangles (pink, blue)Step 3: Area of the full square = a 2−b 2 Step 4: Now we have to find the area of rectangle as shown in the figure.Step 5: Consider the area of pink rectangle = length × breadth = a(a−b)Step 6: Area of blue rectangle = b(a−b) Step 7: Area of full square = area of pink rectangle + area of blue rectangle.i.e., a 2−b 2

Step 1: Draw a square and cut into 3 parts.Step 2: There are 1 hided square green and 2 rectangles (pink, blue)Step 3: Area of the full square = a 2−b 2 Step 4: Now we have to find the area of rectangle as shown in the figure.Step 5: Consider the area of pink rectangle = length × breadth = a(a−b)Step 6: Area of blue rectangle = b(a−b) Step 7: Area of full square = area of pink rectangle + area of blue rectangle.i.e., a 2−b 2 =a(a−b)+b(a−b)a 2 −b 2 =(a+b)(a−b)

Step 1: Draw a square and cut into 3 parts.Step 2: There are 1 hided square green and 2 rectangles (pink, blue)Step 3: Area of the full square = a 2−b 2 Step 4: Now we have to find the area of rectangle as shown in the figure.Step 5: Consider the area of pink rectangle = length × breadth = a(a−b)Step 6: Area of blue rectangle = b(a−b) Step 7: Area of full square = area of pink rectangle + area of blue rectangle.i.e., a 2−b 2 =a(a−b)+b(a−b)a 2 −b 2 =(a+b)(a−b)Hence, geometrically we proved the identity a2−b 2 =(a+b)(a−b).

Answer 2

Answer: Step 1: Draw a square and cut into 3 parts.

Step 2: There are 1 hided square green and 2 rectangles (pink, blue)

Step 3: Area of the full square = a  

2

−b  

2

 

Step 4: Now we have to find the area of rectangle as shown in the figure.

Step 5: Consider the area of pink rectangle = length × breadth = a(a−b)

Step 6: Area of blue rectangle = b(a−b)  

Step 7: Area of full square = area of pink rectangle + area of blue rectangle.

i.e., a  

2

−b  

2

=a(a−b)+b(a−b)

a  

2

−b  

2

=(a+b)(a−b)

Hence, geometrically we proved the identity a  

2

−b  

2

=(a+b)(a−b).